Assuming that we're talking about an extension hosted on Google's extension gallery, there's no mechanism for transferring ownership available in the developer dashboard. Transfers of ownership have to be done manually by someone internally. The extension's owner will need to send an email to the "chromium-extensions" group explaining the situation, and someone from the extensions team will get back with you relatively soon to get the details.
Until there's a better mechanism for this (multiple owners, for instance), I'd suggest that you create a new Google account to share between the extension's owners, and ask for that address to be assigned ownership.